No-arbitrage Pricing of European Options based on Trinomial Tree Model

Abstract

Nowadays, with the rapid development of the financial markets, financial derivatives have been taken more into researchers’ considerations, like Mehrdoust Farshid and Najafi Ali Reza (2017) have tried to find out a semi analytical formula[1]. Unfortunately, it is usually difficult to discover a steady continuous time model to calculate and predict the precise price of an European option. This paper summarizes the meaning of the trinomial tree pricing model, and based on this, from the two aspects of the call option and the put option, obtains the pricing method in line with the characteristics of European options by mathematical deduction. By means of calculating the expectation of certain option to predict a more general conclusion. At last, several potential no-arbitrage prices in different conditions are given in this work, and the deduction formulas of related variables are shown in the conclusions. All options mentioned in this article are options of stocks.